Question

Find x if 5^x+15 (5^0)+5^2+4 (5^x)=665

Answer 1

Hope that helps you.....

Answer 2

The value of x = 3

Given :

$\displaystyle \sf{ {5}^{x} + 15( {5}^{0} ) + {5}^{2} + 4 ({5}^{x}) = 665}$

To find :

The value of x

Solution :

Step 1 of 2 :

Write down the given equation

Here the given equation is

$\displaystyle \sf{ {5}^{x} + 15( {5}^{0} ) + {5}^{2} + 4 ({5}^{x}) = 665}$

Step 2 of 2 :

Find the value of x

$\displaystyle \sf{ {5}^{x} + 15( {5}^{0} ) + {5}^{2} + 4 ({5}^{x}) = 665}$

$\displaystyle \sf{ \implies {5}^{x} + (15 \times 1) + 25 + 4 ({5}^{x}) = 665}$

$\displaystyle \sf{ \implies {5}^{x} + 15 + 25 + 4 ({5}^{x}) = 665}$

$\displaystyle \sf{ \implies {5}^{x} + 40+ 4 ({5}^{x}) = 665}$

$\displaystyle \sf{ \implies {5}^{x} +4 ({5}^{x}) = 665 - 40}$

$\displaystyle \sf{ \implies 5 ({5}^{x}) = 625}$

$\displaystyle \sf{ \implies {5}^{1} \times {5}^{x} = 5 \times 5 \times 5 \times 5}$

$\displaystyle \sf{ \implies {5}^{x + 1} = {5}^{4} }$

$\displaystyle \sf{ \implies x + 1 = 4}$

$\displaystyle \sf{ \implies x = 4 - 1}$

$\displaystyle \sf{ \implies x = 3}$

Hence the required value of x = 3

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